Investment vehicles include various forms, such as, for example, stocks, mutual funds, bonds, options, and exchange-traded funds (ETFs). It should be noted that although the present disclosure uses ETFs as exemplary investment vehicles in the below discussions, the scope of the present invention is not intended to be limited to ETFs. Rather, the methods and systems disclosed in the present invention are also applicable to other forms of investment vehicles, such as, for example, mutual funds, bonds, and options.
An ETF is an investment fund that can be traded, for example, on stock exchanges. An ETF may hold various assets, such as, for example, stocks, funds, bonds, index futures, swaps or short positions, along with cash equivalents. Such assets are hereafter generally referred to as “holdings” of an ETF. Most ETFs track a target base index, for example, the S&P 500® index. A leveraged and/or inverse ETF is designed to achieve a “leverage objective,” that is, a positive or negative multiple of index return on a daily basis (e.g., +2× or −2× of index return). A fund manager may adjust fund holdings each day based on the closing value of fund assets, reflecting index returns and fund flows for that day in order to stay aligned with the +2× or −2× fund multiple goal.
Day-to-day consistency of index exposure, over time, is valuable to many investors. Although a leveraged and/or inverse ETF could be created with a longer-term objective, such as a monthly leverage objective, the ETF's index exposure would then vary within the month, as gains and losses in between monthly rebalancing change the ETF's market exposure. An ETF with a daily leverage objective, say, to be 200 percent exposed to an index, has the objective of providing that same leverage exposure at the end of each and every trading day, regardless of whether an investor bought, held, or sold the ETF position on a particular day. Adjusting holdings every day to match the fund multiple goal (e.g., +2× or −2× of index return) may reduce the risk of the ETF experiencing a total loss. The variation in leverage within the month for a monthly leverage objective could be sizable in higher-volatility environments and may lead to a significantly higher degree of leverage than the investor desires.
Leveraged and/or inverse index exposure in a liquid, transparent ETF can be utilized in a variety of ways, with both short- and longer-term horizons. Since the trading volume for leveraged and/or inverse ETFs, whether measured in dollars or shares, is large, it is likely that leveraged and/or inverse ETFs are commonly being utilized as short-term tactical trading tools. However, investors also regularly use leveraged and/or inverse ETFs as a key component of a longer-term portfolio strategy, for example, to pursue returns and manage the risk of long-term equity and fixed-income positions. The list below identifies a few of the most common applications of the leveraged and/or inverse ETFs all of which can be employed over time:                Implement a tactical view (long or short term) of an index based on an outlook for the economy or segments of the market.        Overweight or underweight an index exposure, such as a particular market-cap segment, sector, or country, by utilizing leverage and thereby avoiding the need to change other positions in the portfolio.        Hedge or reduce risk, either as a short-term tactical hedge or for longer-term risk management.        Execute an index-spread strategy designed to capture the relative returns of two indexes. For example, investors may wish to express a view that financial stocks are likely to outperform energy stocks, or that emerging market equities may outperform U.S. large-cap equities.        Isolate the active risk component of an equity strategy (alpha) from active strategies. Alpha can be isolated by hedging the index or beta risk with a benchmark, e.g., a base level of performance of a certain index, for that strategy using an inverse or leveraged inverse index ETF.        
In an upward-trending market, compounding can result in longer-term returns that are greater than the sum of the individual daily returns. In Table 1, the Index Daily Return column shows that an investment strategy that returns 10 percent per day for two consecutive days generates a 21 percent gain over the two-day period. This is greater than 20 percent, which is the sum of the individual-day returns. Similarly, in a downward-trending market, compounding can also result in longer-term returns that are less negative than the sum of the individual daily returns. An investment that declines 10 percent per day for two consecutive days would have a negative 19 percent return, not negative 20 percent. But in a volatile market scenario, compounding can result in longer-term returns that are less than the sum of the individual daily returns. An investment that rises 10 percent on one day and declines 10 percent the next would have a negative 1 percent return, which is less than the 0 percent sum of the individual-day returns.
Compounding in leveraged funds can result in gains or losses that occur much faster and to a greater degree, as shown in the +2× Fund Daily Return column of Table 1. In an upward-trending market, compounding can result in longer-term leveraged returns that are greater than two times the return of the unleveraged investment. A leveraged fund that grows 20 percent a day (2×10 percent index gain) for two consecutive days would have a 44 percent gain, not two times the 21 percent compound gain of the Index Daily Return.
In a downward-trending market, compounding results in +2× leveraged fund returns that are less negative than two times the return of the unleveraged investment. A +2× leveraged fund that declines 20 percent a day (2×10 percent index decline) for two consecutive days would have a negative 36 percent return. This is less negative than two times the 19 percent compound loss of the unleveraged investment.
TABLE 1Compounding with Unleveraged and Leveraged InvestmentsDayIndex Daily Return+2x Fund Daily ReturnUPWARD TREND1+10%+20%2+10%+20%Compound 2-day Return+21% [+1%] +44% [+4%]DOWNWARD TREND1−10%−20%2−10%−20%Compound 2-day Return−19% [−1%] −36% [−4%]VOLATILE MARKET1+10%+20%2−10%−20%Compound 2-day Return−1% [−1%] −4% [−4%]
In a volatile market, compounding can result in leveraged longer-term returns that are less than two times the return of the unleveraged investment. A +2× leveraged fund that rises 20 percent one day (2×10 percent index gain) and declines 20 percent the next (2×10 percent index decline) generates a negative 4 percent return. This is a greater loss than the two times negative 1 percent compound return of the unleveraged investment.
To better understand how the ETFs behave over time, the inventors analyzed strategies designed to provide +2× and −2× the daily performance of the S&P 500® Daily Objective Strategies over a 50-year time frame, and performed a similar analysis for the NASDAQ-100® and the Dow JonesSM financial and energy sector indexes for somewhat shorter time frames based on availability of historical data. In these analyses, fees, expenses, financing and transaction costs are ignored.
These studies compare the returns of +2× and −2×S&P 500® Daily Strategies with a period return (defined as +2× or −2× the period index return) for holding periods of 2, 7, 30, 91 and 183 calendar days. The sample contains all possible two-day, weekly, monthly, quarterly, and semi-annual holding periods within the past 50 years (1959 through 2008) for the S&P 500® Index. This large sample enables the inventors to compare all possible end-of-day entry and exit points, but it also leads to overlapping observations. The benefit of this approach is that it removes any potential bias of starting a holding period on a particular day of the week or month.
To focus on the compounding effect, some additional assumptions are used in this analysis:
                For the +2× and −2× index returns, the leverage ratio is set at the beginning of each period and not changed for the duration of that period. For the +2× and −2×S&P 500® Daily Strategies, the leverage is reset daily to either +2× or −2×. Therefore, the return achieved by the leveraged and/or inverse Daily Objective Strategies is exactly the daily fund multiple times the daily index return each and every day of the holding periods.        Index price return is the basis for the analysis.        All return calculations exclude fees, financing, interest and expenses.        The +2× and −2× index period returns are not constrained by capital (i.e., losses can exceed negative 100%).        
Table 2 contains statistics from the distribution of differences in return between the Daily Objective Strategy return and +2× and −2× the index return for all possible 2-, 7- and 30-day holding periods over the 50-year S&P 500® return history. The averages of the percentage return differences are all essentially zero, and the median is at or just below zero, indicating that leveraged and/or inverse strategies are about as likely to benefit as to be hurt by the compounding effect for periods up to 30 days for the S&P 500®.
The distribution of the return differences for the +2× and −2×S&P 500® Daily Strategies is tight and balanced over this long history. For example, half of the differences for the +2× Strategy for a 30-day holding period were between 0.1 percent and negative 0.1 percent. This means that for a +2× Strategy over a 30-day period where the S&P 500® return was 3 percent, the returns were in a range of 5.9 percent to 6.1 percent (compared with 2×3 percent, or 6 percent) approximately half the time. In addition, the percentage of positive differences was 53 percent for two-day holding periods. As we move out to longer periods, the return differences are positive about 40 percent of the time.
TABLE 2S&P 500 ® +2x and −2x Daily Strategy vs. +2x and −2x Index Returns+2x Differences−2x DifferencesHolding Periods2 days7 days30 days2 days7 days30 daysAverage0.000% 0.000% −0.002% 0.000% −0.002% −0.035% 97.5th Percentile0.03%0.14% 0.71%0.08% 0.42% 2.08%75th Percentile0.00%0.01% 0.06%0.00% 0.04% 0.19%Median0.00%0.00%−0.03%0.00%−0.01%−0.09%25th Percentile0.00%−0.02% −0.10%0.00%−0.05%−0.29%2.5th Percentile−0.02% −0.12% −0.50%−0.07% −0.35%−1.54%% of Periods 53% 43%   39% 53%   43%   39%PositiveSource: BLOOMBERG ®, based on daily S&P 500 ® Index returns for all possible holding periods between Dec. 31, 1958 and Dec. 31, 2008. For illustrative purposes only.
As seen from the comparative results, the impact of compounding has historically been virtually neutral, with an average effect close to zero and medians close to zero or slightly negative. The overall potential for compounding to lead to positive versus negative effects is approximately equal. There is a high percentage of periods in which S&P 500® Daily Objective Strategies are close to a +2× or −2× leverage ratio over holding periods of a week and a month. The probabilities of getting close to a +2× or −2× realized multiple falls as the holding period lengthens. Leveraged and/or inverse Daily Objective Strategy returns for 7- and 30-day holding periods were, at times, the opposite sign to the period target (a “flipped” return), but this was infrequent.
The largest driver of compounding effects is the level of volatility in the market over the investor's holding period. This point is frequently mentioned in academic, analyst, and media articles when discussing the performance differences for leveraged and/or inverse funds held over time. The long-term study using +2×S&P 500® Daily Strategy returns carried out by the inventors supports the view that volatility is the key factor driving the size of the differences. To explore the connection between volatility and variability of returns over the 50-year S&P 500® return history, inventors first sort the return differences between the 30-day +2×S&P 500® Daily Strategy and the S&P 500® return times two. Inventors then place these return differences into 10 deciles, or “buckets,” ranking them from the most positive to the most negative. For each of these deciles, inventors calculate the median return difference and the median annualized 30-day S&P 500® volatility.
FIG. 1 displays levels of volatility of returns over the 50-year S&P 500® return history and the magnitude of the return difference between the 30-day +2×S&P 500® Daily Strategy and the S&P 500® return times two. As shown in FIG. 1, the holding periods with the most positive and negative deciles of return differences were also ones that have higher volatility. The U-shape of the median volatilities across the return difference deciles reveals that the smallest return differences tend to occur when volatility is lowest. It is notable that the 2008 episode of extreme volatility was the main factor in observing wider return spreads for longer holding periods for the leveraged and/or inverse Daily Objective Strategies.
As shown in FIG. 1, the degree of impact that volatility has on leveraged Daily Objective Strategy returns is relative to the magnitude of the index return for the period. In periods when index return magnitudes are very large, the return differences tend to be large but positive. In contrast, the periods of the most negative differences (0-10th decile) are those where there have been high S&P 500® volatility levels accompanied by index returns close to zero (that is, flat or trendless markets).
In Table 3, data from the inventors' study of +2×Daily Strategy fund returns show the medians for each decile of return differences, along with the median volatility and absolute value of index return for each bucket. Table 3 shows that volatility is not always unwelcome to investors pursuing returns, as higher-magnitude index returns (both positive and negative) are somewhat correlated with higher-volatility market environments.
TABLE 3+2x S&P 500 ® Daily Strategy vs. +2 Times 30-Day Period Index ReturnReturn DifferenceReturnAbsolute Value ofDecileDifferences*S&P 500 ® Return*Index Volatility* 90th to 100th0.47%6.46%14.80%80th to 90th0.17%4.63%11.40%70th to 80th0.07%3.31%9.97%60th to 70th0.02%2.19%9.37%50th to 60th−0.02%0.86%8.95%40th to 50th−0.04%0.32%9.47%30th to 40th−0.06%0.23%11.08%20th to 30th−0.10%0.20%12.41%10th to 20th−0.15%0.09%14.71% 0 to 10th−0.32%0.14%20.43%*All values are medians for each decile. Source: BLOOMBERG ®, based on daily S&P 500 ® Index returns for all possible 30-day holding periods between Dec. 31, 1958 and Dec. 31, 2008. For illustrative purposes only.
FIG. 2 shows the percentage or frequency of realized multiples within selected ranges around +2× and −2×S&P 500® Daily Strategies for every holding period of 2, 7 and 30 days over the 50 years from 1959 to 2008. As shown in FIG. 2, over relatively short holding periods, there has been a high frequency with which +2× and −2×S&P 500® Daily Strategies were closer to their index return times the fund multiple. Observations of long return histories for more volatile indexes show that the frequencies are lower than that for the S&P 500®, but still generally high. The longer the holding period and the more volatile the underlying benchmark, the greater the likelihood that the impact of compounding will cause the returns of a leveraged or inverse Daily Objective Strategies to deviate from the fund multiple.
For leveraged and/or inverse Daily Strategies that track indexes with volatility profiles similar to or lower than the S&P 500®, the analysis indicates that these Daily Strategies have produced realized multiples reasonably close to the +2× or −2× the index return without any rebalancing. For a +2×S&P 500® Daily Strategy, as many as 95 percent of the realized multiples fell within a range of +1.5 to +2.5 (compared with a +2× the index return) over all possible 30-day holding periods. Even higher percentages result for 2- and 7-day horizons. For a −2×S&P 500® Daily Strategy, somewhat fewer (85 percent) realized multiples fell within a negative 1.5 to negative 2.5 multiple range for a 30-day holding period. The frequency of negative multiples for a +2×S&P 500® Daily Strategy and of positive multiples for a −2×S&P 500® Daily Strategy also exists. These multiples are referred to as “flipped.” Flipped multiples happened rarely: less than 1 percent of the 30-day holding periods for a +2×S&P 500® Daily Strategy and about 2 percent for a −2×S&P 500® Daily Strategy.
FIG. 3 shows the realized multiples for longer-term holding periods, including monthly, quarterly and six-month holding periods for +2× and −2×S&P 500® Daily Strategies. For a −2× Strategy, the frequency at which realized multiples fall within a negative 1.5 to negative 2.5 range falls from 85 percent for 30 days to 75 percent for a quarter, and to 70 percent for six months, assuming no rebalancing. The frequency with which returns flip (realized multiples are greater than 0) for the −2×S&P 500® Daily Strategy for a 6-month versus a 30-day holding period rises from 2 percent to 3.4 percent. FIGS. 2 and 3 show a clear connection between the length of the holding period and the probability of achieving a multiple close to the +2× or −2× the index return.
As of mid-2009, more than half of leveraged and/or inverse fund assets in the U.S. were invested in ETFs based on the broad-based equity or fixed-income categories. However, many investors also use leveraged and/or inverse funds tracking U.S. sector indexes with higher return volatility. To evaluate the realized multiples for Daily Objective Strategies with greater historical risk-reward profiles, the inventors calculate realized multiples over a long-term history for 2-, 7- and 30-day holding periods for Daily Objective Strategies with multiples of +2× and −2× for three other indexes: the NASDAQ-100 Index®, the Dow Jones U.S. Financials IndexSM and the Dow Jones U.S. Oil & Gas IndexSM. FIG. 4 shows realized multiples for +2× and −2× Daily Objective Strategies based on the NASDAQ-100 Index®. FIG. 5 shows realized multiples for +2× and −2× Daily Objective Strategies based on the Dow Jones U.S. Oil & Gas IndexSM. FIG. 6 shows realized multiples for +2× and −2× Daily Objective Strategies based on the Dow Jones U.S. Financials IndexSM. These returns do not illustrate the performance of an actual investment.
The history of daily NASDAQ-100 Index® returns begins in 1985, with the index having a return volatility of 28.6 percent over the 1985 to 2008 period. This is significantly higher than the return volatility of 18.3 percent for the S&P 500® over the same period. Comparing FIGS. 2 and 4 reveals that the frequencies of realized multiples for a +2× and −2× NASDAQ-100® Daily Strategy held for 30 days across all multiple ranges are somewhat lower than the S&P 500® due to the higher volatility of the index, but still above 80% (the only exception is the negative 1.75 to negative 2.25 range for the −2× Strategies). For example, as shown in FIG. 4, for a −2× NASDAQ-100® Daily Strategy held 30 days, the negative 1.50 to negative 2.50 realized multiple range frequency was 74.1 percent, compared with 85.3 percent for the S&P 500® leveraged strategy, as shown in FIG. 2.
The Dow Jones U.S. Financials IndexSM and Dow Jones U.S. Oil & Gas IndexSM data are available back to 1992, thus providing 17 years of return experience. The annualized return volatilities based on daily data for each index were 24.85 percent and 24.80 percent, respectively; a bit lower than that of the NASDAQ-100 Index®, but higher than the S&P 500®. Comparing FIGS. 4-6 reveals that the realized multiples for these Daily Objective Strategies are also a bit higher than for the NASDAQ-100 Index®, which is due to the slightly lower return volatilities of the underlying indexes. Therefore, the analysis of higher-volatility indexes further supports the connection between volatility and holding-period risk for holders of leveraged and/or inverse funds with daily fund multiples.
To summarize these findings, there is a high probability that the realized multiples of the Daily Objective Strategies will be close to the fund multiple over time. The shorter the period and the lower the index volatility, the higher the probability. For longer time periods and more volatile benchmarks, the inventors observed lower probabilities. With regard to ETFs, the primary concern of the investors is the performance of leveraged and/or inverse ETFs over time, particularly in a volatile environment. Accordingly, it may be desirable to have methods or systems involving ETFs that may improve the performance of the ETFs over time.